Runge-Kutta-Chebyshev (5,2)
Explicit Runge-Kutta method
Coefficients
\begin{align}
\begin{array}{c|ccccc}
& & & & & \\
\frac{1}{8} & \frac{1}{8} & & & & \\
\frac{1}{8} & \frac{1}{16} & \frac{1}{16} & & & \\
\frac{1}{3} & - \frac{1}{9} & \frac{4}{27} & \frac{8}{27} & & \\
\frac{5}{8} & - \frac{255}{512} & \frac{15}{64} & \frac{5}{8} & \frac{135}{512} & \\
\hline
& - \frac{269}{250} & \frac{8}{25} & \frac{24}{25} & \frac{27}{50} & \frac{32}{125}
\end{array}\end{align}
Properties
- Order of accuracy: $2$
- Stage order: $1$
- Stability function: $$1 + z + \frac{z^{2}}{2} + \frac{7 z^{3}}{80} + \frac{z^{4}}{160} + \frac{z^{5}}{6400}$$
- Radius of absolute monotonicity: $0$
- Principal error norm: 0.110204985771
- Imaginary stability interval: 0
- Real stability interval: 16.8938964088
- Zero-stable: True